It's a bit challenging to teach some of the counter-intuitive notions of geometry in curved spaces. Most lecturers resort to (physical) hand-waving, or some very bad diagrams.

A curved whiteboard would solve this problem. The base would sit horizontally, but the surface would have concave and convex areas, so that it can be shown directly that the angles of a triangle don't always add up to 180 degrees.

(It would be even better if it were flexible, but that's beyond me right now.)
-- Detly, May 19 2004

And where would the teachers go after a hard day of work? http://www.halfbake...bius_20Strip_20Club
[theircompetitor, Oct 04 2004, last modified Oct 05 2004]

Memerase flexible whiteboard http://www.mdcwall....ures/MEBrochure.pdf
Doesn't do convex/concaves though, only bends. [booleanfool, Oct 04 2004, last modified Oct 05 2004]

With my luck I'd inadvertantly dig into an asymptote and generate a rip.
-- dpsyplc, May 19 2004


I think this is completely doable and not a half bad idea. I'll give it a [+]
-- zigness, May 19 2004


Professor Frink: "Oh dear, I've torn the space-time continuum again, class..."
-- Detly, May 19 2004


This idea is totally bent. (+)
-- 2 fries shy of a happy meal, May 19 2004


The globe's good for convex surfaces, but not concave, or combinations.

For the flexible sheet, I thought maybe a chain-mail like structure (like those horrible purses from the 80's), covered in some acrylic sheet. I couldn't figure out how to hold it in place when it was changed, though - I like your idea.
-- Detly, May 20 2004


Mr. Hand: Yes?
Spicoli: I'm registered in this class.
Mr Hand: What class?
Spicoli: This is US history, I see the globe right there.
Mr. Hand: Really?
Spicoli: Really, can I come in?
Mr. Hand: Oh please, I get so lonely when that third attendance bell rings and all of my kids are not here.
-- thumbwax, May 20 2004


“..so you see, in 156 dimensions—”
A hand shoots up. “Ah, professor...”
“Yes?”
“156 dimensions! I can’t visualize that.”
“Well, it’s very simple.” Grinning broadly, the professor deftly pulls and pushes at the Riemann whiteboard. Portions of it seem to glitter with a holographic iridescence as they slip into heretofore unsuspected dimensions. Finally, the Professor stands back, sweating, but pleased with the result.
“Okay now—”
“Professor?”
“Yes yes, surely you see them?”
“Well, I see 155.”
“But not 156?”
“No.”
“Can’t visualize one more dimension?”
“Good Lord no!”
The professor appears to think for a moment, then looks up. “There...there it is--it’s right behind you!”
Student turns.
Professor kicks student’s ass.

-- ldischler, May 20 2004


When I was learning spherical geometry for navigation, we had a globe painted with blackboard paint for this purpose.
-- oneoffdave, May 21 2004


I dread to think what the Equipartition Theorem would have to say about [ldischler]'s scenario.
-- Detly, May 23 2004


I think what you're after is a whiteboard made from a flexible, rubber-like material. Normally this whiteboard would be boringly flat and Cartesian, but when you want to illustrate curved space geometry, just whip out your bicycle pump and pump air into the screen. This inflates the space between the screen and the wall behind, so that the screen bulges away from the wall. You would then be able to draw a triangle on the flat whiteboard and show how the sum of its internal angles changes as you inflate the whiteboard.
-- hippo, May 23 2004


Would that work for concave?
-- Detly, May 23 2004


so Zanzibar Concave is standard in the US
-- engineer1, May 24 2004



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